When you need a strap for your uke so that your left hand has greater freedom, here's a cheap and convenient way to go.
A plastic mini-hook on a strip of adhesive: it has a little tongue that you pull on when you don't want it on your uke any longer: whether after a day, a month or a year, it comes off like a charm and leaves no trace whatever, so it's perfectly harmless to your most treasured possession. Place it on the tail end, slightly off-center (horizontally and vertically closer to your body), attach one end of a shoe-lace to it and the other end just behind the nut.
This way, I was able to splurge on a fluorescent elasticized band which provides even more freedom (and glows in the dark!! -- just kidding, but possibilities are endless).